Acar accelerates uniformly from rest to a speed of 40.0 mi/h in 12.0 s. find (a) the distance the car travels during this time and (b) the constant acceleration of the car.

a) 107.279m

b)

Explanation:

We use the second and third equations of a uniformly accelerated motion as follows;

where u is the initial velocity, v is final velocity, a is acceleration, t is time taken and s is distance covered.

Given;

u = 0m/s (since the car starts from rest)

v =40mi/h

t = 12s

a = ?

s = ?

substituting into equation (1), we obtain the following;

For the purpose of consistency of units, we have to first of all convert the 40mi/h to m/s as follows;

1 mile = 1609.34m

therefore;

40miles = 40 x 1609.34m = 64373.8m

Also,

1 hour = 60 x 60s =3600s.

Hence;

We then make sustitution into equation (2) as follows;

We then proceed to solve for s and a by solving equations (3) and (4) simultaneously.

(a) To find  s, the distance covered;

from equation (3), . We then put this into (4) to obtain the following;

b) As previously stated, ;

hence,

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see earlier answer